The purpose of this project is to improve the remission induction rate of acute lymphocytic leukemia in adult patients utilizing vincristine and dexamethasone with intermittent moderate doses of methotrexate followed by asparaginase. A second objective is to decrease the incidence of severe infections during induction therapy by utilizing oral non-absorbable antibiotics. A third objective is to determine whether intermittent high dose methotrexate with leucovorin rescue and with vincristine and dexamethasone will prolong remission duration. The fourth objective is to determine the efficacy of moderate and high dose methotrexate in preventing meningeal leukemia and to correlate the clinical effectiveness with the cerebrospinal fluid methotrexate levels. To date 26 patients have been entered onto this study. Seventeen patients had no prior treatment, nine had prior treatment. For the no prior treatment patients, four patients are still on study and 13 are off study. For the prior treatment patients, two patients are still on study and 7 patients are off study. For the no prior treatment patients, complete remissions have been achieved in 13 of the 17 (76 percent) patients that went through induction. For the prior treatment patients, seven of nine (78 percent ) achieved complete remission. The median survival for complete remission patients for both groups is 16 plus months and for all treated patients for both groups is 10 plus months.